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Question
Factorise the following by the difference of two squares:
a(a - 1) - b(b - 1)
Sum
Solution
a(a - 1) - b(b - 1)
a2 - a - b2 + b
= a2 - b2 - a + b
= (a2 - b2) - (a - b)
= (a - b)(a + b) - (a - b)
= (a - b)(a + b - 1).
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Method of Factorisation : Difference of Two Squares
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